Finite Group Databasebeta

← C7×D11×D63 #34084708

Subgroups — C7×D11×D63 #34084708

Order 19404.

156 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 156 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×D693C211yesmaximal, characteristic, complemented
2C7×C11×D63C211yesmaximal, characteristic, complemented
3C72×C9×D11C211yesmaximal, characteristic, complemented
4C7×D11×D21—31nomaximal
5C72×C9×C11C2211yescharacteristic, complemented, Hall
6C7×D231—31no—
7C7×C11×D21—31no—
8C3×C72×D11D311yescharacteristic
9D11×D63C711yesmaximal, characteristic, direct product factor
10C7×D9×D11—71nomaximal
11C7×D7×D11—91noHall
12C2×C7×D63—111nomaximal, Hall
13C3×C72×C11C2×D311yescharacteristic
14D693C2×C711yescharacteristic, complemented
15C11×D63C2×C711yescharacteristic, complemented
16C7×D99—71no—
17C7×C11×D9—71no—
18C7×C9×D11—23no—
19C7×C9×D11D711yescharacteristic, complemented
20C7×C9×D11C2×C711yescharacteristic, complemented
21C7×D77—91no—
22C7×C11×D7—91no—
23C72×D11D911yescharacteristic, complemented
24D11×D21—31no—
25D3×C7×D11—211no—
26C2×C72×C9—111no—
27C7×D63—111no—
28C7×D63D1111yescharacteristic, direct product factor
29C7×C9×C11—23no—
30C7×C9×C11C2×D711yescharacteristic, complemented
31C7×C9×C11C22×C711yescharacteristic, complemented
32C2×C7×D21—331no—
33C72×C11C2×D911yescharacteristic, complemented, Hall
34D231—31no—
35C11×D21—31no—
36C7×D33—211no—
37D3×C7×C11—211no—
38C3×C7×D11—23no—
39C3×C7×D11D3×C711yescharacteristic
40C3×C7×D11D2111yescharacteristic
41C72×C9C2×D1111yescharacteristic, complemented, Hall
42D9×D11—71noHall
43C2×C7×D11—631no—
44D7×D11—91no—
45C2×C3×C72—111no—
46C7×D21—31no—
47C7×D21—331no—
48C2×D63—111no—
49C2×C7×D9—771no—
50C3×C7×C11—23no—
51C3×C7×C11C2×D3×C711yescharacteristic
52C3×C7×C11C2×D2111yescharacteristic
53D99—71no—
54C9×D11C7×D711yescharacteristic, complemented
55C11×D9—71no—
56C2×C7×D7—991noHall
57C2×C7×C11—631no—
58D77—91no—
59C7×D11—23no—
60C7×D11—631no—
61C7×D11C7×D911yescharacteristic, complemented
62C7×D11D6311yescharacteristic, direct product factor
63C11×D7—91no—
64C3×C72D3×D1111yescharacteristic
65D3×D11—211no—
66C2×C7×C9—111no—
67C2×C7×C9—111no—
68C2×C7×C9—223no—
69D63—111no—
70D63C7×D1111yescharacteristic, direct product factor
71C7×D9—71no—
72C7×D9—771no—
73C9×C11C2×C7×D711yescharacteristic, complemented, Hall
74C2×C72—111no—
75C7×D7—91no—
76C7×D7—991no—
77C2×D21—331no—
78C2×D3×C7—2311no—
79C7×C11—23no—
80C7×C11C2×C7×D911yescharacteristic, complemented
81C7×C11C2×D6311yescharacteristic, complemented
82D33—211no—
83C3×D11C7×D2111yescharacteristic
84D3×C11—211no—
85C7×C9—23no—
86C7×C9D7×D1111yescharacteristic, complemented
87C7×C9C2×C7×D1111yescharacteristic, complemented
88C72D9×D1111yescharacteristic, complemented, Sylow
89C2×D11—631noHall
90C2×C3×C7—111no—
91C2×C3×C7—111no—
92C2×C3×C7—223no—
93D21—31no—
94D21—331no—
95D3×C7—211no—
96D3×C7—2311no—
97C2×D9—771noHall
98C3×C11C2×C7×D2111yescharacteristic
99C22×C7—6931no—
100C2×D7—991no—
101C2×C11—631no—
102D11—631no—
103D11C7×D6311yescharacteristic, direct product factor
104C3×C7—23no—
105C3×C7D3×C7×D1111yescharacteristic
106C3×C7D11×D2111yescharacteristic
107C2×C9—111no—
108D9—71no—
109D9—771no—
110C2×C7—111no—
111C2×C7—111no—
112C2×C7—223no—
113C2×C7—631no—
114C2×C7—6931no—
115D7—91no—
116D7—991no—
117C2×D3—2311no—
118C11C2×C7×D6311yescharacteristic, complemented, Sylow
119C9C7×D7×D1111yescharacteristic, complemented, Sylow
120C7—23no—
121C7C7×D9×D1111yescharacteristic, complemented
122C7D11×D6311yescharacteristic, direct product factor
123C2×C3—111no—
124D3—211no—
125D3—2311no—
126C22—6931noSylow
127C3C7×D11×D2111yescharacteristic
128C2—111no—
129C2—631no—
130C2—6931no—
subgroupG/H
center, hypercenterC7D11×D63
commutator, cosocle, hypocenterC7×C9×C11C22×C7
FrattiniC3C7×D11×D21
FittingC72×C9×C11C22
socleC3×C72×C11C2×D3
LCSG ▷ C7×C9×C11
UCSC1 ◁ C7

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C7×D693C2semidirect
2. C7×C11×D63C2semidirect
3. C72×C9×D11C2semidirect
5. C72×C9×C11C22semidirect
9. D11×D63C7direct (N × H)
14. D693C2×C7semidirect
15. C11×D63C2×C7semidirect
19. C7×C9×D11D7semidirect
20. C7×C9×D11C2×C7semidirect
23. C72×D11D9semidirect
28. C7×D63D11direct (N × H)
30. C7×C9×C11C2×D7semidirect
31. C7×C9×C11C22×C7semidirect
33. C72×C11C2×D9semidirect
41. C72×C9C2×D11semidirect
54. C9×D11C7×D7semidirect
61. C7×D11C7×D9semidirect
62. C7×D11D63direct (N × H)
70. D63C7×D11direct (N × H)
73. C9×C11C2×C7×D7semidirect
80. C7×C11C2×C7×D9semidirect
81. C7×C11C2×D63semidirect
86. C7×C9D7×D11semidirect
87. C7×C9C2×C7×D11semidirect
88. C72D9×D11semidirect
103. D11C7×D63direct (N × H)
118. C11C2×C7×D63semidirect
119. C9C7×D7×D11semidirect
121. C7C7×D9×D11semidirect
122. C7D11×D63direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C7×D6932
C7×C11×D632
C72×C9×D112
C7×D11×D213
D11×D637
C7×D9×D117
C2×C7×D6311